Question

A current I is passing through a wire having two sections P and Q of uniform diameters d and $d/2$ respectively if the mean drift velocity of electrons in section P and Q is denoted by and respectively then.

Answer 1

$I=neAvd$

so, drift velocity will be

$vd=\frac{I}{neA}$

here

$A=\pi r2$

so,

$vd=\frac{I}{ner\pi 2}$

now,

if the radius is doubled

$v{d}^{\prime }=\frac{I}{ne\pi r^{\prime }2}=\frac{I}{ne\pi (2r{)}^2}$

thus, we get

$v{d}^{\prime }=\frac{1}{4}\times \frac{I}{ner\pi 2}$

or

$v{d}^{\prime }=\frac{vd}{4}$